Discrete fractional diffusion equation. (English) Zbl 1345.65067
Summary: The tool of the discrete fractional calculus is introduced to discrete modeling of diffusion problem. A fractional time discretization diffusion model is presented in the Caputo-like delta’s sense. The numerical formula is given in form of the equivalent summation. Then, the diffusion concentration is discussed for various fractional difference orders. The discrete fractional model is a fractionization of the classical difference equation and can be more suitable to depict the random or discrete phenomena compared with fractional partial differential equations.
MSC:
| 65Q10 | Numerical methods for difference equations |
| 76R50 | Diffusion |
| 35R11 | Fractional partial differential equations |
| 39A14 | Partial difference equations |
| 26A33 | Fractional derivatives and integrals |
| 37M05 | Simulation of dynamical systems |
Keywords:
discrete fractional calculus; discrete anomalous diffusion; discrete fractional partial difference equationsReferences:
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